First, to define terms, we will say that the Romantic Era of English poetry encompassed the years 1785 to 1830 and the "modern" era encompasses anything written after 1900. This division fails to distinguish between modernism and post-modernism, but as far as poetry goes, modernist qualities carry into the post-modern (after 1950) era.
Romantic poetry is characterized by the use of traditional verse forms and Romantic themes. Traditional verse forms such as sonnets, ballads, and odes as well as other forms such as ottava rima and Alexandrine verse have in common that they use consistent rhythm and meter throughout the poem and have a regular rhyme scheme or follow blank verse (unrhymed iambic pentameter) forms. The topics and themes of Romantic poetry were individualism, awe of nature, importance of imagination, strong emotions, and an interest in the common man and childhood. Representative examples are Wordsworth's sonnet "The World Is Too Much with Us," Keats' "Ode on a Grecian Urn," Shelley's "Adonais," Coleridge's "Rime of the Ancient Mariner," and Byron's "Don Juan." In addition, the lyrical ballad, introduced by Wordsworth and Coleridge, redirected poetry during the Romantic era to be more accessible to everyday readers.
In the Modern era, the most notable change is the replacement of traditional verse forms by the rhythms and language of normal speech. Imagism, a movement started by Ezra Pound, tended toward minimalism in poetry, and while not all modern poets were Imagists, many adopted the free verse format and the sparse wording of that movement. "Oread" by H.D. is an example of an Imagist poem. T. S. Eliot is representative of modern poetry in "The Wasteland" and "The Hollow Men." Not only do these poems use modernist language in using irregular rhythms, rhyme schemes, and stanzas, but they also reflect the pessimistic or uncertain outlook of the 20th century. Poetry became deliberately obscure, as with Wallace Stevens' "The Emperor of Ice Cream," and experimented with capitalization and punctuation, as with E. E. Cummings' "In Just-." Fragmented thoughts and disjointed perspectives are common in Modernist poetry as well. Poetry in this era favors questions over pat answers, as in Yeats' "Second Coming."
The major differences in Romantic and Modernist poetry are their forms and the preferred subject matter and perspective.